Which option correctly represents L = {1, 8, 27, 64, 125}?
Answer and explanation
Correct answer: L = {x : x = n³, n ∈ ℕ, 1 ≤ n ≤ 5}
The governing idea is set-builder representation: describe every member by a rule and restrict the parameter to the required values. The listed numbers are consecutive cubes: 1 = 1³, 8 = 2³, 27 = 3³, 64 = 4³, and 125 = 5³. Therefore x = n³ with 1 ≤ n ≤ 5 gives exactly the five listed elements. Option B gives squares, option C gives multiples of 3, and option D gives infinitely many cubes. Hence A is correct.
Frequently asked questions
What is the correct answer to this question?
L = {x : x = n³, n ∈ ℕ, 1 ≤ n ≤ 5}
Why is this the correct answer?
The governing idea is set-builder representation: describe every member by a rule and restrict the parameter to the required values. The listed numbers are consecutive cubes: 1 = 1³, 8 = 2³, 27 = 3³, 64 = 4³, and 125 = 5³. Therefore x = n³ with 1 ≤ n ≤ 5 gives exactly the five listed elements. Option B gives squares, option C gives multiples of 3, and option D gives infinitely many cubes. Hence A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
